Skip to main content
SpringerLink
Log in

Bounds on degrees of projective schemes

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Achilles, R., Huneke, C. and Vogel, W.: A criterion for intersection multiplicity one. Nagoya Math. J.100, 49–63 (1985)

    Google Scholar 

  2. Amoroso, F.: Test d'appartenance d'après un théorèm de Kollár. C.R. Acad. Sci. Paris309, 691–695 (1989)

    Google Scholar 

  3. Bayer, D. and Mumford, D.: What can be computed in algebraic geometry? In: Eisenbud, D. and L. Robbiano, L. (eds.): “Computational Algebraic Geometry and Commutative Algebra”, Proceedings Cortona 1991, Cambridge University Press, 1993, pp. 1–48

  4. Berenstein, C.A. and Yger, A.: Bounds for the degrees in the division problem. Michigan Math. J.126, 25–43 (1990)

    Google Scholar 

  5. Brownawell, D.: Bounds for the degrees in the Nullstellensatz. Annals of Math.126, 577–592 (1987)

    Google Scholar 

  6. Brownawell, D.: Note on a paper of P. Philippon. Michigan Math. J.34, 461–464 (1987)

    Google Scholar 

  7. Caniglia, L., Galligo, A. and Heintz, J.: Borne simple exponentielle pour les degrés dans le théorèm des zeros sur un corps de charactéristique quelconque. C.R. Acad. Sci. Paris307, 255–258 (1988)

    Google Scholar 

  8. Eisenbud D.: Commutative Algebra with a View Towards Algebraic Geometry, Graduate Texts in Mathematics, Springer, New York 1994

    Google Scholar 

  9. Eisenbud, D. and Harris, J.: Schemes: The Language of Modern Algebraic Geometry. Belmont, Wadsworth: 1992

    Google Scholar 

  10. Flenner, H. and Vogel, W.: On multiplicities of local rings. Manuscripta math78, 85–97 (1993)

    Google Scholar 

  11. Fulton, W.: Intersection Theory. Berlin Heidelberg New York, Springer: 1984

    Google Scholar 

  12. Gröbner, W.: Moderne Algebraische Geometrie. Wien, Springer Verlag: 1949

    Google Scholar 

  13. Hartshorne, R.: Connectedness of the Hilbert scheme. Publicat. I.H.E.S.29, 261–304 (1966)

    Google Scholar 

  14. Kalkbrener, M. and Sturmfels, B.: Initial complexes of prime ideals. Advances in Mathematics, to appear

  15. Kollár, J.: Sharp effective Nullstellensatz. Journal A.M.S.1, 963–975 (1988)

    Google Scholar 

  16. Philippon, P.: Lemmes de zéros dans les groupes algébriques commutatifs. Bull. Soc. Math. France114, 335–383 (1986)

    Google Scholar 

  17. Renschuch, B. and Vogel, W.: Perfektheit und die Umkehrung des Bezoutschen Satzes. Math. Nachrichten148, 313–323 (1990)

    Google Scholar 

  18. Shiffman, B.: Degree bounds for the division problem in polynomial ideals. Michigan Math. J.36, 163–171 (1989)

    Google Scholar 

  19. Stückrad, J. and Vogel, W.: Buchsbaum Rings and Applications. Berlin Heidelberg New York, Springer: 1986

    Google Scholar 

  20. Sturmfels, B.: Gröbner bases of toric varieties. Tohoku Math. J.43, 249–261 (1991)

    Google Scholar 

  21. Thomas, R.: A geometric Buchberger algorithm for integer programming, Mathematics of Operations Research, to appear.

  22. Vogel, W.: Lectures on results on Bezout's Theorem. (Lecture Notes, Tata Institute of Fundamental Research, Bombay, No. 74) Berlin Heidelberg New York, Springer: 1984

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, 94720, Berkeley, CA, USA

    Bernd Sturmfels

  2. Institute of Mathematics, Bò Hô, P.O. Box 631, Hanoi, Vietnam

    Ngô Viêt Trung

  3. Department of Mathematics, Massey University, Palmerston North, New Zealand

    Wolfgang Vogel

Authors
  1. Bernd Sturmfels
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ngô Viêt Trung
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wolfgang Vogel
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sturmfels, B., Ngô Viêt Trung & Vogel, W. Bounds on degrees of projective schemes. Math. Ann. 302, 417–432 (1995). https://doi.org/10.1007/BF01444501

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01444501

Mathematics Subject Classification (1991)

Search

Navigation